We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed ...
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We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of the number of observations. The significance of the expression is that it provides us with a linear-time algorithm to compute the finite predictor coefficients. In the proof of the expression, a correspondence result between two relevant matrix-valued outer functions plays a key role. We apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes. (C) 2019 Elsevier Inc. All rights reserved.
Proposes a parallel randomized algorithm, called PFAST (Parallel Fast Assignment using Search Technique), for scheduling parallel programs represented by directed acyclic graphs (DAGs) during compile-time. The PFAST a...
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ISBN:
(纸本)9780818680908
Proposes a parallel randomized algorithm, called PFAST (Parallel Fast Assignment using Search Technique), for scheduling parallel programs represented by directed acyclic graphs (DAGs) during compile-time. The PFAST algorithm has O(e) time complexity, where e is the number of edges in the DAG. This linear-time algorithm works by first generating an initial solution and then refining it using a parallel random search. Using a prototype computer-aided parallelization and scheduling tool called CASCH (Computer-Aided SCHeduling), the algorithm is found to outperform numerous previous algorithms while taking dramatically smaller execution times. The distinctive feature of this research is that, instead of simulations, our proposed algorithm is evaluated and compared with other algorithms using the CASCH tool with real applications running on an Intel Paragon. The PFAST algorithm is also evaluated with randomly generated DAGs for which optimal schedules are known. The algorithm generated optimal solutions for a majority of the test cases and close-to-optimal solutions for the others. The proposed algorithm is the fastest scheduling algorithm known to us and is an attractive choice for scheduling under running time constraints.
We introduce and study the problem MUTUAL DUALITY, asking for two planar graphs G1 and G2 whether G1 can be embedded such that its dual is isomorphic to G2. We show NP-completeness for general planar graphs and give a...
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